Robustness of optimal decision rules where one of the team members is exceptionally qualified

This work investigates the robustness of optimal decision rules under a changing size of a decision group where the competence of one member is outstanding while the others possess an identical competence. More specifically, we focus on the expert rule, the almost expert rule and the tie-breaking chairperson rule. We first establish criteria for the optimality of each of these rules and then use it to investigate their robustness. Robustness is an important property of decision rules, especially when cost of adjustment to a new rule is high. Our findings are that the expert rule and the chairperson rule are robust while the almost expert rule is not.

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Justification of the simple majority and chairman rules

Employing the uncertain dichotomous model, this work proves the optimality of the simple majority and the chairman rules under complete ignorance of the decision competencies of the decision makers. The optimality of these commonly used rules is also retained under certain patterns of partial information on the characteristics of the distribution of the members' competencies.     

Optimality among restricted majority decision rules

When a group of decision makers with common interests faces a dichotomous choice, the task of deciding may be delegated to a committee consisting of a subset of the original group. This procedure is called a restricted majority decision rule. If each member of the original group is characterized by the probability of his deciding correctly, the expected utility from the decision is determined by which members are appointed to the committee. The conditions between enabling the comparison of alternative restricted majority rules are based on the voting profiles of the decision makers. The purpose of the current study is to propose an algorithm for identifying the optimal restricted majority rule amongst all restricted majority rules.I am indebted to Shmuel Nitzan for helpful comments and suggestions. All shortcomings are, of course, entirely my responsibility.     

Robustness of optimal majority rules over teams with changing size

This work investigates the robustness of optimal restricted majority rules under a changing size of a decision group. Robustness is an important property of decision rules, especially when cost of adjustment to a new rule is high. This is most likely to be the case when information about the competence of the members of the decision team is not costless. One of the useful findings of this study is that optimal restricted majority rules are robust over reductions of the decision team.The authors appreciate comments made by four anonymous referees.     

Optimum committee size: Quality-versus-quantity dilemma

According to Condorcet, the larger the team of decision-makers using the simple majority rule, the more likely they are to reach correct decisions. This paper examines the validity of this claim under the condition of reduced team competence with size. Determining committee size always involves quality-versus-quantity dilemma. This study provides criteria, as well as an algorithm, for deciding on the optimum size of boards and committees. Received: 18 January 2002/Accepted: 22 April 2002 The authors acknowledge the helpful comments of an anonymous referee.     

A note on restricted majority rules: invariance to rule selection and outcome distinctiveness

Recently, Karotkin (1993) has shown that in the symmetric uncertain dichotomous choice model the set of restricted majority rules (RMRs) is special in the sense that a member of this family of rules is always the worst rule among the potentially optimal weighted majority rules (WMRs). In the current paper we establish two additional special properties of RMRs. First, given a particular configuration of the group members' decisions, the collective choice is invariant to the selection of WMRs if it is invariant to the selection of RMRs. Second, given a particular decision profile, a potentially optimal WMR can result in a distinctive collective choice which is different from the choice of any other potentially optimal WMR, if and only if it is a RMR.     

The essential ranking of decision rules in small panels of experts

For small panels of experts (e.g., boards of managers, courts, specialized committees), n 5, this paper provides an algorithm for ranking the seven efficient and commonly used weighted majority rules by their respective performance. These rules are terned efficient since they constitute the set of potentially optimal decision rules in uncertain, symmetric, pairwise choice situations. The main contribution of this study is the discovery of an essential ordering of six of these rules which entails that the set of possible ranking of the seven rules is almost single peaked.The essential ordering significantly reduces the number of possible rankings of the rules, and thus, simplifies the development of the ranking algorithm. The essential ordering has important applications when the available information on the experts' decisional skills is incomplete.